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geometric analysis 1isocapacitary inequality 1mean curvature 1metric measure spaces 1RCD spaces 1willmore inequality 1

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math.DG2026

Mean curvature and sharp Willmore inequalities in metric spaces

Nicola Gigli, Ivan Yuri Violo

The paper defines a notion of mean curvature for level sets of Sobolev functions in non‑smooth metric spaces with Ricci curvature bounded below, introduces a Willmore functional, a…